The 27-year-old defender has signed a four-year contract at Turf Moor after helping Sheffield United secure promotion to the Premier League in 2023.
“I’m really happy to be here,” he told club website.
“I’ve played at Turf Moor against Burnley before and it’s always been a really good atmosphere, I’m excited to call it home.
“I know the Championship from my time in the league and I’m looking forward to using my experience to help the team. I can’t wait to get started.”
Ahmedhodzic began his career with his hometown club before joining Nottingham Forest’s academy in 2016.
He made his professional debut against Newcastle United at just 17 before returning to Malmo in 2019.
